Bertini theorems for F-singularities

Published 9 Dec 2011 in math.AG and math.AC | (1112.2161v5)

Abstract: We prove that strongly F-regular and F-pure singularities satisfy Bertini-type theorems (including in the context of pairs) by building upon a framework of Cumino, Greco and Manaresi (compare with the work of Jouanolou and Spreafico). We also prove that F-injective singularities fail to satisfy even the most basic Bertini-type results.

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